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C2×C3×C72×AGL(1,𝔽11) #44568749

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3×C72×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C3×C5×C72)
unambiguous semidirect product(C2×D11)⋊(C3×C5×C72)
unambiguous semidirect product(C11⋊C5)⋊(C22×C3×C72)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C3×C72)
unambiguous semidirect product(C2×C3×D11)⋊(C5×C72)
unambiguous semidirect product(C2×C3×C7×D11)⋊(C5×C7)
unambiguous semidirect product(C2×C3×C72×D11)⋊C5

Splittings

Fitting, socleC2×C3×C72×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C3×C5×C72
HallC3×C72×C11⋊C5 ⋊ C22
HallC2×C3×C72×D11 ⋊ C5
HallC72×C11⋊C5 ⋊ C22×C3
HallC2×C72×D11 ⋊ C3×C5
HallC3×C72×C11 ⋊ C22×C5
HallC72×C11 ⋊ C22×C3×C5
HallC3×C11⋊C5 ⋊ C22×C72
HallC2×C3×D11 ⋊ C5×C72
HallC11⋊C5 ⋊ C22×C3×C72
HallC2×D11 ⋊ C3×C5×C72
HallC3×C11 ⋊ C22×C5×C72

Subgroups

subgroupG/H
center, hypercenterC2×C3×C72AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C3×C5×C72
FrattiniC1G
Fitting, socleC2×C3×C72×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C72

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3234

Conjugacy classes & character table

3234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 451);